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Full text of "Mathematical And Physical Papers - Iii"

94     ON  THE  EFFECT  OF THE INTERNAL  FRICTION  OF  FLUIDS
or, since ml is so small that we may neglect m*}
The long pendulum furnishes a similar equation, and the result obtained from the brass sphere is
(156),
since 2  ^ is the quantity which is regarded as accurately known. The ivory sphere in like manner furnishes the equation
l',-l\............(157),
where the accented letters refer to that sphere. The equation for the determination of k results from the elimination of X between the equations (156) and (157).
Now, according to the theory of this paper, the factor k has really different values for the long and short pendulums. Let /^ refer to the short, and kz to the long pendulum with the brass sphere, &/ to the short, and &2' to the long pendulum with the ivory sphere. Then
m
and therefore

(l 58). v      7
In the equation resulting from the elimination of \ between (156) and (157), let the values of 12 - ^ and / - Z/ got from (158) and the similar equation relating to the ivory sphere be substituted. The result is
m
This equation is of the form
P 4- Qwi, + Em,2 = F + QX + and P = P',  and   Rm*,  R'm* may  be  neglected,  so that the